Areas of Triangles-Gr 6-Solved Examples

Solved Examples and Worksheet for Areas of Triangles

Q1Find the area of a triangle whose base is 5 in. and height is 6 in.
A. 17 in²
B. 19 in²
C. 15 in²
D. 14 in²

Solutions

Step: 1

Area of a triangle = 12 × base × height

Step: 2

= 12 × 5 × 6

[Substitute base = 5 and height = 6.]

Step: 3

= 302 = 15

[Simplify.]

Step: 4

The area of the triangle is 15 in².

Correct Answer is : 15 in²

Q2What is the area of the triangle, if the height of the triangle is two times the base and the base length is 9 m?

A. 7 m²
B. 11 m²
C. 81 m²
D. 13 m²

Solutions

Step: 1

Area of the triangle = 12 × base × height

Step: 2

The height of the triangle is two times the length of the base.

Step: 3

Height of the triangle = 2 × base length = 2 × 9 = 18 m

[Substitute base length = 9.]

Step: 4

Area of the triangle = 12 × 9 × 18

[Substitute the values.]

Step: 5

= 9 × 9 = 81

[Simplify.]

Step: 6

The area of the triangle is 81 m².

Correct Answer is : 81 m²

Q3Find the area of the triangle whose height is 6 ft and base is three times its height.
A. 59 ft²
B. 108 ft²
C. 49 ft²
D. 54 ft²

Solutions

Step: 1

The area of the triangle = 12 × base × height

[Formula.]

Step: 2

The base length = 3 × height
= 3 × 6 = 18 ft

[Since base is three times the height.]

Step: 3

So, area of the triangle = 12 × 18 × 6

[Substitute the values.]

Step: 4

= 1082

[Simplify.]

Step: 5

= 54 ft²

[Divide the numerator and the denominator by 2.]

Step: 6

Area of the triangle = 54 ft².

Correct Answer is : 54 ft²

Q4BC is 6 cm and the height of the triangle ABC is 5 cm. Find the area of the shaded region of the figure, if the area of the triangle DEF is 5 cm².

A. 13 cm²
B. 10 cm²
C. 12 cm²
D. 11 cm²

Solutions

Step: 1

Area of the shaded region of the figure = area of the triangle ABC - area of the triangle DEF

Step: 2

Area of a triangle with base b and height h = 12 × b × h

Step: 3

The area of the triangle ABC = 12 × BC × height of the triangle ABC = 12 × 6 × 5.

[Substitute BC = 6 cm and height = 5 cm.]

Step: 4

= 302 = 15 cm²

[Simplify.]

Step: 5

The area of the shaded region of the figure = 15 - 5

[Substitute the areas of the triangles.]

Step: 6

= 10 cm²

[Subtract.]

Step: 7

The area of the shaded region of the figure = 10 cm².

Correct Answer is : 10 cm²

Q5X, Y and Z are the mid-points of the corresponding sides of the isosceles triangle ABC. What is the area of the shaded region, if AB = 6 m, BC = 8 m, XP = 2 m and the area of the triangle ABC is 16 m²?

A. 33 m²
B. 18 m²
C. 8 m²
D. 16 m²

Solutions

Step: 1

In the figure, BY = YC = BC2 = 82 = 4 m

[Since Y is the midpoint of BC.]

Step: 2

Area of the parallelogram XBYZ = base x height = BY × XP

Step: 3

= 4 × 2 = 8 m²

[Substitute BY = 4 and XP = 2.]

Step: 4

Area of the shaded region = Area of the triangle ABC - Area of the parallelogram XBYZ

Step: 5

= 16 - 8 = 8 m²

[Substitute and subtract.]

Correct Answer is : 8 m²

Q6What is the height of the triangle, if the base of the triangle is twice the height, and its area is 225 yd²?

A. 15 yd
B. 19 yd
C. 16 yd
D. None of the above

Solutions

Step: 1

Let h is the height of the triangle.

Step: 2

Given, area of the triangle = 225 yd²
The base = twice the height = 2 × h.

Step: 3

Area of a triangle = 12 × base × height

[Formula.]

Step: 4

225 = 12 × 2 × h × h

[Substitute the values.]

Step: 5

225 = h²

[Simplify.]

Step: 6

225 = h2

[Taking square root on both sides.]

Step: 7

15 = h

Step: 8

The height of the triangle = 15 yd.

Correct Answer is : 15 yd

Q7AB is the diameter of the circle. What is the area of the shaded region in the figure?[π = 3.14.]

A. 58.04 in.²
B. 85 in.²
C. 83.04 in.²
D. None of the above

Solutions

Step: 1

Base of the triangle = 12 in. and the height of the triangle = 5 in.

[Figure.]

Step: 2

The area of ΔABC = 12 × base × height

[Formula.]

Step: 3

= 12 × 12 × 5

[Substitute the values.]

Step: 4

= 30

[Multiply.]

Step: 5

The area of the triangle ABC = 30 in.²

Step: 6

Area of the circle = π(d2)²

[Formula.]

Step: 7

= 3.14 × (122)²

[Substitute the values.]

Step: 8

= 3.14 × 6²

Step: 9

= 113.04

[Simplify.]

Step: 10

The area of the circle = 113.04 in.²

Step: 11

Area of the shaded region = area of the circle - area of the triangle ABC

Step: 12

= 113.04 - 30

[From Steps 5 and 10.]

Step: 13

= 83.04

Step: 14

So, the area of the shaded region is 83.04 in.²

Correct Answer is : 83.04 in.²

Q8What is the area of the triangle ABC in the figure?

A. 4 square units
B. 3 square units
C. 8 square units
D. 6 square units

Solutions

Step: 1

From the figure, base of the triangle is 2 units, and its height is 3 units.

Step: 2

Area of triangle = 12 × base × height

[Formula.]

Step: 3

Area of the triangle ABC

= 12 × 2 × 3

[Substitute the values.]

Step: 4

= 3 square units

Step: 5

Area of the triangle ABC = 3 square units.

Correct Answer is : 3 square units

Q9Find the area of the triangle, if a = 32 ft, b = 40 ft, and c = 24 ft.

A. 960 ft²
B. 768 ft²
C. 384 ft²
D. 480 ft²

Solutions

Step: 1

Area of a triangle with base b and height h = 12 × b × h

Step: 2

From the figure, base of the triangle = BC = 32 ft and height of the triangle = AB = 24 ft

Step: 3

Area of the triangle ABC = 12 × 32 ft × 24 ft = 384 ft²

[Substitute the values and simplify.]

Step: 4

The area of the triangle = 384 ft².

Correct Answer is : 384 ft²

Q10What is the area of the triangle?

A. 820 cm²
B. 360 cm²
C. 184.5 cm²
D. 180 cm²

Solutions

Step: 1

Base of the triangle is 9 cm and its height is 40 cm.

Step: 2

Area of a triangle = 12 × base × height

Step: 3

= 12 × 9 × 40

Step: 4

= 180

Step: 5

Area of the triangle is 180 cm².

Correct Answer is : 180 cm²

Q11What is the area of the triangle?

A. 240 cm²
B. 280 cm²
C. 160 cm²
D. 560 cm²

Solutions

Step: 1

Base of the triangle is 35 cm and height is 16 cm.

Step: 2

Area of a triangle = 12 × base × height

Step: 3

= 12 × 35 × 16

Step: 4

= 280

[Simplify.]

Step: 5

So, area of the triangle is 280 cm².

Correct Answer is : 280 cm²

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